Here are the canonical forms of Hamiltonian equations, in both the most familiar real form
and the complex form,
which is often conveniently in situations involving either Schroedinger’s equation or other conservative equations involving complex quantities, such as in optics.
The two forms are connected by the change of variables
where one has to allow the quantities and to have complex values.
Why this post?
- Because I can: posting to a blog hosted at WordPress is the only option I currently know of that allows mathematical notation to be used (via latex-like mark-up) when posting to a web-site from a mobile device like this iPad
- To do something work-related with this employer-provided iPad … though I do also use it for all my in-class PDF presentations
- To advertise my upcoming colloquium talk on numerical methods for solving such equations in a way that respects all conservation laws: Friday November 18; details at math.cofc.edu/colloquium